Լոգարիթմ

x = log₂7

55.

log₃(81) = 4

log₂(16) = 4
log₀.₁(1000) = -3
log₀.₀₀₁(0.001) = -3

lg 0.001 = log₁₀(0.001) = -3

log₂(⁵√4) = log₂(⁵√(2²)) = log₂(2^(2/5)) = 2/5

lg(100/√10) = lg(100) – lg(√10) = 2 – (1/2)lg(10) = 2 – (1/2) * 1 = 2 – 0.5 = 1.5

log(100/√10) = lg(10²/10^(1/2)) = lg(10^(2/3)) = log₁₀(10^(2/3)) = 3/2

log₅(25³√5) = log₅(5² * 5^(1/3)) = log₅(5^(7/3)) = 7/3

log(1/7, 49√7) = log(1/7, 7² * 7^(1/2)) = -5/2

57.

5^ ( 2log5base12)=(5^(log5base12)²=12²=144
a^(log a base b)= b

b) 8°(4log8base3)=(8^(log8base3)⁴= 3⁴=81

c) 7^(0,5log7base16)=(7^(log7base16)= 16^½=√16 =4

d) 9^(log3base8)= 3^(2log3base8) =(3^(log3base8)²=8²=64

58 log₄(8) = log₂(2²) = 2

4^x=8

3^(2x)= 2³

2x= 3

X= 3/2